A Robin-type non-overlapping domain decomposition procedure for second order elliptic problems

This article deals with the analysis of an iterative non-overlapping domain decomposition (DD) method for elliptic problems, using Robin-type boundary condition on the inter-subdomain boundaries, which can be solved in parallel with local communications. The proposed iterative method allows us to relax the continuity condition for Lagrange multipliers on the inter-subdomain boundaries. In order to derive the corresponding discrete problem, we apply a non-conforming Galerkin method using lowest order Crouzeix–Raviart elements. The convergence of the iterative scheme is obtained by proving that the spectral radius of the matrix associated with the fixed point iterations is less than 1. Parallel computations have been carried out and the numerical experiments confirm the theoretical results established in this paper.     

Effect of Host Substitution on Photochemical Properties of Pyrene/β-Cyclodextrin Solid Complexes

Pyrene/β-cyclodextrin solid complexes (prepared using β-cyclodextrin, hydroxypropyl-β-cyclodextrin, and 2,3,6-triacetyl-β-cyclodextrin as hosts) were characterized by means of fluorescence spectroscopy and time-resolved diffuse reflectance laser flash photolysis. The relative intensity of the 0–0 and 0–2 vibronic bands in the emission spectrum of pyrene is found to increase as substitution of the cyclodextrin hydroxyl groups increases. Furthermore, a concomitant shortening in pyrene triplet lifetime results. Interestingly, a significant decrease in pyrene radical anion yield and lifetime is observed with 2,3,6-triacetyl-β-cyclodextrin as host; this effect is ascribed to the potential ability of the host matrix to trap electrons.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.